Question

find tu.
tu =

Explanation:

Step1: Determine the similarity of triangles

Since \( TQ\parallel SR\) (by the mid - segment property indicated by the congruent marks on the sides), \(\triangle TQU\sim\triangle SRU\).

Step2: Use the similarity ratio

The ratio of the sides of similar triangles is equal. The ratio of \( QU\) to \( RU\) is \(\frac{QU}{RU}=\frac{60 - 40}{60}=\frac{20}{60}=\frac{1}{3}\). Let \( TU = x\), and \( SU=72\). Then \(\frac{TU}{SU}=\frac{QU}{RU}\). Substituting the values, we have \(\frac{x}{72}=\frac{1}{3}\).

Step3: Solve for \(x\)

Cross - multiply: \(3x = 72\). Then \(x=\frac{72}{3}=24\).

Answer:

\(24\)